Solving system of first order linear differential equations

I wanted to solve a system of first order linear differential equations in MATLAB. Expressed in terms of matrices, the equation is of the form . In this equation, the matrix C is a constant matrix which can be determined from the user input. So the solution to this equation if of the form for each eigenvalue of the matrix, and its corresponding eigenvector . My aim is to plot the dependent variables in the system as functions of time.

So I know the command eig to get the eigenvalues and corresponding eigenvectors. After getting these, how do I express the set of variables as per the equation above. Assume that the constants can be determined from initial conditions.

Note: I also saw that ode45 can be used in this case, but I wanted to learn how to express the equation using symbols in MATLAB. Any help will be appreciated. TIA

[madhan ravi]

posting the datas of your equation would help

Answer 1

[Star Strider]

You can use the numeric solvers if that works for you. It may be easier to use the expm (link) function for a linear problem such as this. Don’t worry about the eigenvalues — expm has already implemented the Cayley-Hamilton Theorem for you with respect to the matrix exponential.